vote is keep the bucket on. more so in unfamiliar territory. bucket can make for a good detector for stuff out in front of you in tall weeds that you can not see through. granted you will most likely push what ever is in front of you over and down into dirt. but it can save your "radiator", tires possibly, underneath tractor from large branch suddenly veering up into tractor as you roll over it. to not cutting stuff up with rotatory cutter.
the rotatory cutter should have slip clutch that has been adjusted and set correctly (more so if it has been setting for some time, double check slip clutch) or at min a shear bolt. and hopefully some sort of "stump jumper blade setup underneath it. so if you do hit something with rotatory cutter it does not harm the cutter.
if you do take bucket off, keep the "arms" of the FEL on for front counter weight, for the bush hog. or if you take entire FEL off, put some suit case weights or like on the front.
i think legally you can have something hanging out the back a couple feet. but do not quote me, regs/laws change to much from area to area.
suggest making sure you chain/strap the tractor down, the FEL down, and rotatory cutter down to the trailer. it kinda of a pain to add extra chains / straps. but hit a few bumps or make some sharp turns or what not, or something rarely happening, and you could be in some big trouble.